Method and apparatus for performing floating point arithmetic operation and rounding the result thereof

Abstract

An apparatus uses a sticky digit in rounding an interim solution Yr into a final approximate solution Ye for an infinite precise solution Y, determined by a function F according to Y=F(X) with respect to digital data X. The apparatus includes a partial product generator receiving a multiplicand and a multiplier, at least one of which represents an interim solution Yr, for generating a plurality of partial products; a sign inversion generator for generating a sign inversion value, expressed in the same format as the partial products, from at least a lower part of a subtrahend to enable place matching, where the subtrahend represents the digital data X; an adder for adding the partial products and the sign inversion value; a detector which, in response to the addition result, detects whether the subtrahend or a product of the multiplicand and multiplier is greater; and a sticky digit generator for generating the sticky digit in response to the detection result.

What is claimed is: 
     
       1. An apparatus for generating a sticky digit used in rounding an interim solution Yr into a final approximate solution Ye for an infinite precise solution Y determined by a function F according to Y=F(X) with respect to digital data X, the apparatus comprising: means for generating a plurality of partial products from a given multiplicand and a given multiplier, wherein at least one of the given multiplicand and the given multiplier represents an interim solution Yr;   means for generating a sign inversion value from at least a lower part of a subtrahend to enable place matching, the sign inversion value expressed in a same format as a format of expression of the partial products, the subtrahend representing digital data X;   means for adding the partial products and the sign inversion value;   means for detecting which of the subtrahend and a product of the given multiplicand and the given multiplier is greater in response to a result of said adding by said adding means; and   a sticky digit generating means for generating a sticky digit in response to a result of said detecting by said detecting means.   
     
     
       2. An apparatus for generating a sticky digit used in rounding an interim solution Yr into a final approximate solution Ye for an infinite precise solution Y determined by a function F according to Y=F(X) with respect to digital data X, the apparatus comprising: multiplying means for performing a multiplication of a multiplicand and a multiplier, wherein at least one of said multiplicand and said multiplier represents an interim solution Yr, and   sticky digit generating means connected for receiving a product output from said multiplying means and for providing a sticky digit,   wherein said multiplying means includes: means for generating a plurality of partial products from said multiplicand and said multiplier;   means for generating a sign inversion value from at least a lower part of a subtrahend to enable place matching, the sign inversion value expressed in a same format as a format of expression of the partial products, said subtrahend representing digital data X; and   means for adding the partial products and the sign inversion value,   wherein said sticky digit generating means comprises means for generating a sticky digit in response to a result of said adding by said adding means in said multiplying means.     
     
     
       3. An apparatus as recited in claim 2, wherein said sticky digit generating means comprises means for providing said sticky digit in response to a determination of which of the subtrahend and a product of the multiplicand and the multiplier is greater.   
     
     
       4. An apparatus as recited in claim 2, wherein said sticky digit generating means comprises means for detecting which of the subtrahend and a product of the multiplicand and the multiplier is greater in response to a result of said adding by said adding means; and   means for providing said sticky digit in response to a detection by said detecting means of which of the subtrahend and a product of the multiplicand and the multiplier is greater.